HLib is a library for hierarchical matrices that was written by Lars Grasedyck and Steffen Börm. Most routines are written in the C programming language using BLAS and LAPACK for lower-level algebraic operations. The library contains functions for H- and H2-matrix arithmetics, the treatment of partial differential equations and a number of integral operators as well as support routines for the creation of cluster trees, visualization and numerical quadrature. This is a work in progress, so there may be undiscovered errors and you can expect new features to appear with every new release.

References in zbMATH (referenced in 75 articles , 1 standard article )

Showing results 21 to 40 of 75.
Sorted by year (citations)
  1. Glau, Kathrin; Mahlstedt, Mirco: Improved error bound for multivariate Chebyshev polynomial interpolation (2019)
  2. Karkulik, Michael; Melenk, Jens Markus: (\mathscrH)-matrix approximability of inverses of discretizations of the fractional Laplacian (2019)
  3. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  4. Shepherd, David; Miles, James; Heil, Matthias; Mihajlović, Milan: An adaptive step implicit midpoint rule for the time integration of Newton’s linearisations of non-linear problems with applications in micromagnetics (2019)
  5. Börm, Steffen: Adaptive compression of large vectors (2018)
  6. Dölz, Jürgen; Harbrecht, Helmut: Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains (2018)
  7. Feischl, Michael; Kuo, Frances Y.; Sloan, Ian H.: Fast random field generation with (H)-matrices (2018)
  8. Xing, Xin; Chow, Edmond: Preserving positive definiteness in hierarchically semiseparable matrix approximations (2018)
  9. Betcke, Timo; van’t Wout, Elwin; Gélat, Pierre: Computationally efficient boundary element methods for high-frequency Helmholtz problems in unbounded domains (2017)
  10. Börm, Steffen; Melenk, Jens M.: Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis (2017)
  11. Chávez, Gustavo; Turkiyyah, George; Keyes, David E.: A direct elliptic solver based on hierarchically low-rank Schur complements (2017)
  12. Corona, Eduardo; Rahimian, Abtin; Zorin, Denis: A tensor-train accelerated solver for integral equations in complex geometries (2017)
  13. Dölz, J.; Harbrecht, H.; Peters, M. D.: (\mathcalH)-matrix based second moment analysis for rough random fields and finite element discretizations (2017)
  14. Dölz, J.; Harbrecht, H.; Schwab, Ch.: Covariance regularity and (\mathcalH)-matrix approximation for rough random fields (2017)
  15. Pan, Victor Y.: Fast approximate computations with Cauchy matrices and polynomials (2017)
  16. Vasconcelos, Paulo B.: Data-sparse approximation on the computation of a weakly singular Fredholm equation: a stellar radiative transfer application (2017)
  17. Ballani, Jonas; Kressner, Daniel: Matrices with hierarchical low-rank structures (2016)
  18. Börm, Steffen; Christophersen, Sven: Approximation of integral operators by Green quadrature and nested cross approximation (2016)
  19. Falletta, Silvia; Sauter, Stefan A.: The panel-clustering method for the wave equation in two spatial dimensions (2016)
  20. Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk: Existence of (\mathcalH)-matrix approximants to the inverses of BEM matrices: the simple-layer operator (2016)

Further publications can be found at: http://www.hmatrix.org/literature.html